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Braess's Paradox

When building more roads makes traffic WORSE

THE PARADOX

Adding a new road to a traffic network can increase EVERYONE's travel time! Selfish routing leads to a Nash equilibrium that's worse for all. Sometimes REMOVING roads improves traffic.

🛣️ THE SHORTCUT ROAD
Average Travel Time
45 min

Network Statistics

Total Drivers 4000
Top Route (A→B→D) 0
Bottom Route (A→C→D) 0
A→B (T/100 min) 20 min
B→D (45 min fixed) 45 min
A→C (45 min fixed) 45 min
C→D (T/100 min) 20 min

⚖️ Nash Equilibrium

Without shortcut: Drivers split evenly. Each route = 45 + 20 = 65 min. Equilibrium!

🧮 The Mathematics

Consider 4000 drivers going from A to D. Two routes exist:

Top: A→B→D where T(AB) = drivers/100
Bottom: A→C→D where T(CD) = drivers/100
Fixed roads: 45 minutes each

Without shortcut: 2000 take each route. Time = 45 + 20 = 65 min

With FREE shortcut B→C: Everyone takes A→B→C→D. Time = 40 + 0 + 40 = 80 min!

🎯 Why Does This Happen?

Each driver makes the selfish optimal choice. With the shortcut available:

  • Taking A→B is always better than A→C (variable vs 45 min)
  • Taking C→D is always better than B→D (variable vs 45 min)
  • Everyone chooses A→B→C→D
  • The congestion-dependent roads get ALL traffic

Result: A "free" road makes everyone 15 minutes late!

🌍 Real-World Examples

🇰🇷
Seoul, South Korea
Demolishing Cheonggyecheon Expressway IMPROVED traffic and created a 5-mile park!
🇺🇸
New York City
Closing 42nd Street for Earth Day 1990 reduced congestion. Broadway closures became permanent plazas!
🇩🇪
Stuttgart, Germany
New road in 1969 worsened traffic until a section was closed again.

🏀 Beyond Traffic

Braess's Paradox appears in many systems:

  • Power grids: Adding transmission lines can cause blackouts
  • Basketball: A star player can reduce team efficiency (everyone passes to them)
  • Internet routing: More bandwidth can slow networks
  • Spring networks: Adding springs can increase displacement

In random networks, adding an edge causes Braess's Paradox with probability ~50%!

📜 History

1920: Arthur Pigou first noticed the phenomenon

1968: Dietrich Braess at Ruhr University formally described it while modeling traffic

2005: Seoul demolishes expressway, confirming the paradox

2009: NYC creates permanent pedestrian plazas after successful street closures

💡 The Lesson

When individuals optimize selfishly, the group outcome can be suboptimal. This is a multi-player Prisoner's Dilemma.

Solutions include:

  • Congestion pricing (make the shortcut costly)
  • Removing roads (!)
  • Centralized routing (GPS coordination)
  • Converting roads to pedestrian zones